Problem: What is the degree of the polynomial $(3x^2 +11)^{12}$?
Explanation: The degree of the polynomial is the degree of the highest term.  Since the degree of $3x^2 +11$ is 2 and since $(x^a)^{12} = x^{12a}$ for any positive constant $a$, the answer is $2 \cdot 12 = \boxed{24}$.